Epitrochoids

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A disk of radius rolls around the outside of the circumference of a unit circle, while a pen fixed on the disk traces out a"Spirograph™" pattern. The pen's distance from the center of the rolling disk is
.
Contributed by: Bruce Fast (March 2011)
Open content licensed under CC BY-NC-SA
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An epitrochoid is traced by a point attached to a circle of radius rolling around the outside of a fixed circle of radius
, where the point is at a distance
from the center of the exterior circle. The Spirograph™ toy, using toothed gears, is constrained to a set of rational values for
, giving closed curves. Here,
and
is constrained to rational values
. Animating the parameter
portrays the familiar drawing mechanism.
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